Electrical resistivity and thermoelectric power of copper-germanium films

Electrical resistivity and thermoelectric power of copper-germanium films

Thin Solid Films, 58 (1979) 339-343 0 Elsevier Sequoia S.A., Lausanne-Printed 339 in the Netherlands ELECTRICAL RESISTIVITY AND THERMOELECTRIC COPP...

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Thin Solid Films, 58 (1979) 339-343 0 Elsevier Sequoia S.A., Lausanne-Printed


in the Netherlands



P. NATHt Department of Physics and Measurement (Sweden)


University of hinkbping, S;SSI 83 Linkiiping

K. L. CHOPRA Department of Physics, Indian Institute of Technology, New Delhi 110029 (Indib)

(Received July 24, 1978: accepted September 14, 1978)

Cu-Ge films over the whole composition range were prepared by the vapour quenching of the alloys onto glass substrates held at 300 K. The electrical resistivity, thermoelectric power and temperature dependence of the films were studied in the temperature range 100-500 K. The observed behaviour of the electrical resistivity and thermoelectric power is understandable on the basis of transmission electron microscopy and electron diffraction observations which indicate three structural regions. Up to 5 at.% Ge in copper the films are single phase with a structure similar to that of pure copper; in the range 5-80 at.% Ge in copper the films consist of a mixture of Cu,Ge, copper and germanium; beyond 80 at.% the Cu-Ge films are single-phase amorphous.


The preparation and properties of thin films of mixtures of metals and insulators or semiconductors are of significant importance because of the potential industrial applications’,2. The structura12,3, electronic2*4 and superconducting2 behaviour of metal-metal oxide films have been studied in high metal concentration (granular) films and at low metal concentrations. In contrast with the large number of reports available on metal-metal oxide codeposits’ very little is known about metal-semiconductor codeposits. In this paper we present some results of studies on the electronic properties of thin films of germanium codeposited with copper over the whole composition range. 2. EXPERIMENTAL DETAILS Cu-Ge mixtures were obtained by melting the high purity (99.99%) constituents in an alumina crucible for 1 h in a vacuum of about 10e6 Torr. Thin films were obtained by thermal evaporation in a vacuum of about 10m6 Torr from a tungsten basket onto clean glass and freshly cleaved rock-salt substrates maintained at room temperature. High rates of evaporation (>20 .A s-r) were employed to *Paper presented at the Fourth International Congress on Thin Films, Loughborough, September 11_15,1978;Paper4B14. I’ Formerly at the Department of Physics, Indian Institute of Technology, Delhi, India.

Gt. Britain,




maintain the stoichiometry of the films. The reproducibility of the data in films prepared sequentially from the same melt demonstrated the constancy of the composition of the films. The structural order and microstructure of the films were determined by transmission electron microscopy gnd electron diffraction. The electrical resistivity of the films in the temperature range 100-500 K was measured with either a Keithley electrometer or a digital ohmmeter in the conventional manner. The experimental arrangement used to measure the thermoelectric power (TEP) of these films with respect to copper electrodes as a function of temperature was similar to that described by Chopra and Bahl’. 3.



Transmission electron microscopy and electron diffraction studies showed that the CuGe films are homogeneous amorphous in the composition range from germanium to germanium+20 at.% Cu. The films exhibit halo-type electron diffraction patterns essentially similar to that of amorphous germanium. This type of behaviour has been observed for germanium codeposited with several metals6*7. For copper concentrations greater than 20 at.% the diffraction patterns are a mixture of the patterns for randomly mixed but segregated microcrystallites of germanium, copper and Cu,Ge. A detailed discussion of this structural behaviour is presented in ref. 8. For pure copper films and alloys with germanium concentrations up to 5 at.% the electron diffraction patterns indicate the existence of a polycrystalline single-phase homogeneous solid solution of germanium impurity in copper with an f.c.c. structure. Figure 1 shows the compositional dependence of the electrical resistivity and relative TEP of Cu-Ge films. The addition of germanium to copper causes the resistivity to increase monotonically, rapidly at first and then gradually. In the amorphous state (beyond 80 at.% Ge) the electrical resistivity increases very rapidly. Similarly, the addition of 2 at.% Ge to copper causes the relative TEP to become negative and to increase gradually. At the polycrystalline-to-amorphous transformation the TEP increases rapidly to values as high as 200 uV K-‘. Figure 2 shows the temperature dependence of the electrical resistivity of the Cu-Ge films. The resistivity changes from increasing with temperature to decreasing with temperature. Figure 3 shows the temperature dependence of the TEP for our films. In general the TEP increases with increasing temperature, the increase becoming more rapid with increasing germanium concentration. Amorphous Cu-Ge films exhibit a complicated temperature dependence. Initially the TEP increases with increasing temperature and then it decreases rapidly to become increasingly negative. The inversion temperature (i.e. the temperature at which the TEP changes sign) is found to increase with increasing germanium concentration. Such a behaviour for germanium has been previously reported in ref. 9. For small concentrations of germanium in copper the electrical resistivity and the TEP (Fig. 2) behaviour are’tmderstandable in terms of conventional theories of impurity scattering. The contribution to the resistivity by germanium impurity can be estimated from Matthiessen’s rule. It is independent of temperature and increases





linearly with impurity concentration; the value of 3.75 @2 (at.%)- ’ that we obtained is nearly the same as that observed in the corresponding bulk system”. Using the Nordheim-Gortor relation the characteristic TEP for germanium impurity in copper was estimated to be 0.86 uV K-‘. A detailed analysis of the electronic properties of various dilute germanium alloys has been described by Chopra et al.’ ” l2 With further increase in the germanium concentration (beyond 20 at.%), thermally activated tunnelling of electrons between isolated metallic particles becomes a significant parallel conduction mechanism. This results in a decrease and a change in sign of the temperature coefficient of resistance. For concentrations greater than 50 at.% the tunnelling mechanism dominates the conduction process.



Ge Concentration

of Ge

(At %)



Fig.1. The concentration dependence of the electrical resistivity and TEP of Cu-Ge films. Fig. 2. The temperature dependence of the electrical resistivity of Cu-Ge films.

To understand the transport behaviour of amorphous Cu-Ge films, let us first consider amorphous germanium (a-Ge). Extensive studiesI have shown that conduction in a-Ge is due to the phonon-assisted hopping of carriers at the Fermi level at low temperatures ( < 300 K). However, excitation from extended states of the valence band to extended states of the conduction band dominates conduction at high temperatures. The problem of hopping conduction in amorphous materials has been treated by Mott14 and othersI and a temperature dependence of the form logp cc 1/T”4 is predicted. The data for a-Ge fit the Mott T-l” relation. The addition of copper modifies the conduction behaviour drastically. Conduction may occur (a) by thermally assisted hopping in a manner similar to that in a-Ge and other amorphous semiconductors’4 at low temperatures and/or (b) by activated charge carrier tunnelling2 from one metal island to another if the metal is segregated in the form of microclusters. The former mechanism will lead to a 1/T”4 dependence



of the electrical resistivity whereas the latter mechanism yields a l/T 16*17or a l/T”’ ’ dependence. To establish the validity of the various mechanisms, the data for amorphous Cu-Ge films are given in Fig. 4 in the forms log p versus l/T, log p versus 1/T’12 and log p uersus l/T ‘I4 . It is clear that the electrical resistivity data for amorphous Cu-Ge films yield a reasonable fit to Mott’s T- 114relation of variable range hopping for low concentrations of germanium ( < 10 at.%).








.04 (K)

.26 l/T’”

80% .m


(K.‘“) 06



Fig. 3. The temperature dependence of the TEP of Cu-Ge films. Fig. 4. Plots oflogp US.l/T(O), logp vs. l/T”’ (m)and logp vs. 1/T’j4 (0) for amorphous CuCIe films.

For large (> 10 at.%) concentrations of copper in germanium, microsegregation and clustering of copper atoms may occur. The conduction in such amorphous films may be treated in a manner analogous to conduction in discontinuous (granular) metal films. The problem of conduction in metal island films has been treated by Neugebauer and Webbi and Hartman”. The most plausible conduction mechanism in such films is activated charge carrier creation and tunnelling. This mechanism leads to a l/T dependence of the resistivity. Recently the problem of conduction in insulator-rich films has been treated by Abeles2 who obtained a l/T II2 dependence of the electrical resistivity. On the basis of the present data it is difficult to decide between these relations. Although a quantitative interpretation of the TEP of amorphous materials is not possible at present, the TEP of amorphous Cu-Ge alloys is qualitatively understandable in terms of bipolar conduction in localized and extended states. The low temperature behaviour of a-Ge and Ge-Cu (copper concentration less than 5 at.%) can be explained in terms of hopping in the localized states at the Fermi level. The inversion of sign and the high temperature behaviour of the TEP can be understood in terms of a combination of hopping in the localized states and bandlike conduction due to electrons and holes in the extended states.




REFERENCES 1 J. I. Gittleman, B. Abeles, P..Zanzucchi and Y. Arie, Thin Solid Films, 45 (1977) 9. B. Abeles, in R. Wolfe (ed.), Applied S&id State Science, Academic Press, New York, 1976, p. 1. 3 P_Nath, J. E. Sundgren and H. T. G. Nilsson, Phys. Status Solidi A, 48 (1978) 345. 4 J. J. Hauser, Phys. Rev., 7 ( 1973) 4099. 5 K. L. Chopra and S. K. Bahl, Thin Solid Films, 12 (1972) 211. 6 K. L. Chopra, P. Nath and A. C. Rastogi, Phys. Status Solidi A, 27( 1975) 645. 7 H. S. Randhawa, P. Nath, L. K. Malhotra and K. L. Chopra, SolidSrate Commun., 20 (1976) 73. 8 V. Dutta, P. Nath and K. L. Chopra, Phys. Sfatus Solidi A, 48 (1978) 257. 9 K. L. Chopra and S. K. Bahl, Phys. Rev., Seer. B, I (1970) 2545. 10 J.O.Linde,Ann.Phys.,Z0(1932)52:14(1932)355:/5(1932)219. 11 K. L. Chopra, R. Suri and A. P. Thakoor, Phys. Rev., Serf. B, 15 (1977) 4682. 12 K. L. Chopra and A. P. Thakoor, J. Appl. Phys., 49 (1978) 2855. 13 K. L. Chopra, P. Nath and D. K. Pandya, Indian J. Phys., I (1976) 9. 14 N. F. Mott and E. A. Davis, Electronic Processes in Non-Crystalline Materials, Clarendon Press, London, 1973. 15 V. Ambegeokar, B. M. Halperin and T. S. Longer, J. Non-Cryst. Solids, 8-10 (1972) 472. 16 C. A. Neugebauer and M. B. Webb, J. Appt. Phys., 33 ( 1962) 74. 17 T. E. Hartman, J. Appl. Phys., 34 (1963) 943. 2